train <- read.csv("../../../data/train.csv")
test <- read.csv("../../../data/test.csv")
# copy the test and train data sets for EDA
train.c1 <- train
test.c1 <- test
train.c1$datetime = ymd_hms(train.c1$datetime)
test.c1$datetime = ymd_hms(test.c1$datetime)
train.c1 <- train.c1 %>%
mutate(year = as.factor(format(datetime, format = "%Y")),
# month = as.factor(format(datetime, format = "%m")),
month = month(train.c1$datetime, label = TRUE, abbr = FALSE),
day = as.factor(format(datetime, format = "%d")),
hour = as.factor(format(datetime, format = "%H")),
season = factor(season, labels = c("Spring", "Summer", "Fall", "Winter")),
holiday = factor(holiday, labels = c("No", "Yes")),
workingday = factor(workingday, labels = c("No", "Yes")),
weather = factor(weather, labels = c("Great", "Good", "Average", "Poor")))
test.c1 <- test.c1 %>%
mutate(year = as.factor(format(datetime, format = "%Y")),
# month = as.factor(format(datetime, format = "%m")),
month = month(test.c1$datetime, label = TRUE, abbr = FALSE),
day = as.factor(format(datetime, format = "%d")),
hour = as.factor(format(datetime, format = "%H")),
season = factor(season, labels = c("Spring", "Summer", "Fall", "Winter")),
holiday = factor(holiday, labels = c("No", "Yes")),
workingday = factor(workingday, labels = c("No", "Yes")),
weather = factor(weather, labels = c("Great", "Good", "Average", "Poor")))
| Column Name | Type | Description |
|---|---|---|
| 1. datetime | Character | YYYY-MM-DD HH24 (example: 2011-01-01 04:00:00) |
| 2. season | Integer | (1-4) |
| 3. holiday | Integer | (0 or 1) |
| 4. workingday | Integer | (0 or 1) |
| 5. weather | Integer | (1-4) |
| 6. temp | Float | temparture in Celcius |
| 7. atemp | Float | “feels like” temperature in Celsius |
| 8. humidity | Integer | relative humidity |
| 9. windspeed | Float | wind speed |
| 10. casual | Integer | count of casual users |
| 11. registered | Integer | count of registered users |
| 12. count | Integer | count of total users (primary response variable) |
train.c1 %>%
remove_missing(na.rm = TRUE) %>%
group_by(month) %>%
ggplot(aes(x = month, y = count, fill=month)) +
geom_bar(position = "dodge", stat = "summary", fun = "mean") +
ggtitle("Bar Plot of Average Hourly Bike Rentals by Month") +
labs(x = "Month", y = "Average") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
train.c1 %>%
ggplot(aes(x=month, y=count, fill=month)) +
geom_boxplot() +
ggtitle("Box Plot of Bike Rentals by Month") +
labs(x = "Month", y = "Average") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
train.c1 %>%
remove_missing(na.rm = TRUE) %>%
group_by(season) %>%
ggplot(aes(x = season, y = count, fill=season)) +
geom_bar(position = "dodge", stat = "summary", fun = "mean") +
ggtitle("Bar Plot of Average Hourly Bike Rentals by Season") +
labs(x = "Season", y = "Average") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
train.c1 %>%
ggplot(aes(x=season, y=count, fill=season)) +
geom_boxplot() +
ggtitle("Box Plot of Bike Rentals by Season") +
labs(x = "Season", y = "Average") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
train.c1 %>%
remove_missing(na.rm = TRUE) %>%
group_by(hour) %>%
ggplot(aes(x = hour, y = count, fill=hour)) +
geom_bar(position = "dodge", stat = "summary", fun = "mean") +
ggtitle("Bar Plot of Average Bike Rentals by Hour") +
labs(x = "Hour", y = "Average") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
train.c1 %>%
ggplot(aes(x=hour, y=count, fill=hour)) +
geom_boxplot() +
ggtitle("Box Plot of Bike Rentals by Hour") +
labs(x = "Hour", y = "Average") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
train.c1 %>%
remove_missing(na.rm = TRUE) %>%
group_by(weather) %>%
ggplot(aes(x = weather, y = count, fill=weather)) +
geom_bar(position = "dodge", stat = "summary", fun = "mean") +
ggtitle("Bar Plot of Average Hourly Bike Rentals by Weather") +
labs(x = "Weather", y = "Average") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
train.c1 %>%
ggplot(aes(x=weather, y=count, fill=weather)) +
geom_boxplot() +
ggtitle("Box Plot of Bike Rentals by Weather") +
labs(x = "Weather", y = "Average") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
train.c1 %>%
remove_missing(na.rm = TRUE) %>%
group_by(workingday) %>%
ggplot(aes(x = workingday, y = count, fill=workingday)) +
geom_bar(position = "dodge", stat = "summary", fun = "mean") +
ggtitle("Bar Plot of Average Hourly Bike Rentals by Working Day") +
labs(x = "Working Day", y = "Average") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
train.c1 %>%
ggplot(aes(x=workingday, y=count, fill=workingday)) +
geom_boxplot() +
ggtitle("Box Plot of Bike Rentals by Working Day") +
labs(x = "Working Day", y = "Average") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
train.c1 %>%
remove_missing(na.rm = TRUE) %>%
group_by(holiday) %>%
ggplot(aes(x = holiday, y = count, fill=holiday)) +
geom_bar(position = "dodge", stat = "summary", fun = "mean") +
ggtitle("Bar Plot of Average Hourly Bike Rentals by Holiday") +
labs(x = "Holiday", y = "Average") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
train.c1 %>%
ggplot(aes(x=holiday, y=count, fill=holiday)) +
geom_boxplot() +
ggtitle("Box Plot of Bike Rentals by Holiday") +
labs(x = "Holiday", y = "Average") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
train.c1.numeric <- train.c1 %>%
select_if(is.numeric)
corr <- round(cor(train.c1.numeric), 1)
ggcorrplot(corr, method = "circle")
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.
train.c1 %>%
ggplot(aes(x = registered, y = count)) +
geom_point(alpha = 0.3) +
geom_smooth(method = 'lm') +
ggtitle("Line Chart of Counts by Registered Users") +
labs(x = "Registered", y = "Count")
## `geom_smooth()` using formula 'y ~ x'
train.2012.june <- train.c1 %>%
filter(train.c1$year == 2012 & train.c1$month == "June")
ggplot(data=train.2012.june, aes(x = datetime, y = count)) +
geom_line() +
ggtitle("Hourly Rental Trends for June 2012") +
labs(x = "Time", y = "Count")
plotts.sample.wge(train.2012.june$count)
## $autplt
## [1] 1.000000000 0.828532930 0.546215266 0.321994901 0.157437698
## [6] -0.001661608 -0.168661853 -0.298425387 -0.336504623 -0.279103753
## [11] -0.270570795 -0.326233915 -0.362975203 -0.342110136 -0.300595184
## [16] -0.302699276 -0.331757312 -0.289079884 -0.169029889 -0.025179530
## [21] 0.111734895 0.251322989 0.429583910 0.643519434 0.767846516
## [26] 0.663108155
##
## $freq
## [1] 0.002192982 0.004385965 0.006578947 0.008771930 0.010964912 0.013157895
## [7] 0.015350877 0.017543860 0.019736842 0.021929825 0.024122807 0.026315789
## [13] 0.028508772 0.030701754 0.032894737 0.035087719 0.037280702 0.039473684
## [19] 0.041666667 0.043859649 0.046052632 0.048245614 0.050438596 0.052631579
## [25] 0.054824561 0.057017544 0.059210526 0.061403509 0.063596491 0.065789474
## [31] 0.067982456 0.070175439 0.072368421 0.074561404 0.076754386 0.078947368
## [37] 0.081140351 0.083333333 0.085526316 0.087719298 0.089912281 0.092105263
## [43] 0.094298246 0.096491228 0.098684211 0.100877193 0.103070175 0.105263158
## [49] 0.107456140 0.109649123 0.111842105 0.114035088 0.116228070 0.118421053
## [55] 0.120614035 0.122807018 0.125000000 0.127192982 0.129385965 0.131578947
## [61] 0.133771930 0.135964912 0.138157895 0.140350877 0.142543860 0.144736842
## [67] 0.146929825 0.149122807 0.151315789 0.153508772 0.155701754 0.157894737
## [73] 0.160087719 0.162280702 0.164473684 0.166666667 0.168859649 0.171052632
## [79] 0.173245614 0.175438596 0.177631579 0.179824561 0.182017544 0.184210526
## [85] 0.186403509 0.188596491 0.190789474 0.192982456 0.195175439 0.197368421
## [91] 0.199561404 0.201754386 0.203947368 0.206140351 0.208333333 0.210526316
## [97] 0.212719298 0.214912281 0.217105263 0.219298246 0.221491228 0.223684211
## [103] 0.225877193 0.228070175 0.230263158 0.232456140 0.234649123 0.236842105
## [109] 0.239035088 0.241228070 0.243421053 0.245614035 0.247807018 0.250000000
## [115] 0.252192982 0.254385965 0.256578947 0.258771930 0.260964912 0.263157895
## [121] 0.265350877 0.267543860 0.269736842 0.271929825 0.274122807 0.276315789
## [127] 0.278508772 0.280701754 0.282894737 0.285087719 0.287280702 0.289473684
## [133] 0.291666667 0.293859649 0.296052632 0.298245614 0.300438596 0.302631579
## [139] 0.304824561 0.307017544 0.309210526 0.311403509 0.313596491 0.315789474
## [145] 0.317982456 0.320175439 0.322368421 0.324561404 0.326754386 0.328947368
## [151] 0.331140351 0.333333333 0.335526316 0.337719298 0.339912281 0.342105263
## [157] 0.344298246 0.346491228 0.348684211 0.350877193 0.353070175 0.355263158
## [163] 0.357456140 0.359649123 0.361842105 0.364035088 0.366228070 0.368421053
## [169] 0.370614035 0.372807018 0.375000000 0.377192982 0.379385965 0.381578947
## [175] 0.383771930 0.385964912 0.388157895 0.390350877 0.392543860 0.394736842
## [181] 0.396929825 0.399122807 0.401315789 0.403508772 0.405701754 0.407894737
## [187] 0.410087719 0.412280702 0.414473684 0.416666667 0.418859649 0.421052632
## [193] 0.423245614 0.425438596 0.427631579 0.429824561 0.432017544 0.434210526
## [199] 0.436403509 0.438596491 0.440789474 0.442982456 0.445175439 0.447368421
## [205] 0.449561404 0.451754386 0.453947368 0.456140351 0.458333333 0.460526316
## [211] 0.462719298 0.464912281 0.467105263 0.469298246 0.471491228 0.473684211
## [217] 0.475877193 0.478070175 0.480263158 0.482456140 0.484649123 0.486842105
## [223] 0.489035088 0.491228070 0.493421053 0.495614035 0.497807018 0.500000000
##
## $db
## [1] -4.80083688 1.73342930 2.95912507 -8.92683985 -8.69073421
## [6] -5.66744729 2.94645627 -3.35250420 2.11975229 -2.34448113
## [11] -4.79856214 -2.57332785 -12.19521424 0.77418576 -0.34262160
## [16] 4.64444849 -6.33193241 -4.81482165 20.49417880 -5.16165867
## [21] -2.79857225 2.39701596 -13.25644029 -10.03861616 -2.55903082
## [26] -2.75691994 -3.24578552 -6.83013406 -11.03850134 -16.10784667
## [31] -17.06518317 -6.93981202 5.88179973 1.17468825 9.74665038
## [36] 2.58254416 0.88803320 14.04606652 -1.22326834 2.30809642
## [41] 7.78739671 -0.95766747 2.74212477 -1.98262810 -14.20858749
## [46] -18.15232404 -9.29856734 -13.48263068 -4.46252096 -11.83475173
## [51] -4.15609522 -1.85859776 -9.69423024 -2.50105261 -5.01382094
## [56] -5.17140433 9.17446380 -15.08544252 -9.93327318 0.62351328
## [61] -5.69921245 -5.58796163 -13.31053346 -21.72562613 -8.95851291
## [66] -20.42546777 -12.23537556 -15.74587653 -15.22595232 -10.51304770
## [71] -9.09719326 -11.33061737 -1.60677375 -14.89905898 -14.90762213
## [76] 5.50205224 -9.21424894 -4.09548557 -2.80172718 -10.15956755
## [81] -5.76756475 -10.44116910 -16.16036343 -11.63004726 -10.18053450
## [86] -13.75559850 -10.24599621 -21.06588811 -7.38865741 -2.32618833
## [91] -10.72133135 0.69976441 -4.68631873 -11.17618178 9.85357239
## [96] -18.12838344 -5.56789139 -0.02963042 -6.66657705 -3.02233722
## [101] -17.01439209 -24.16596079 -13.30802867 -21.03290775 -20.00637067
## [106] -13.98763122 -17.05282259 -7.76858271 -11.56386807 -29.11448395
## [111] -11.93514820 -14.04054133 -14.34497743 -1.80896074 -11.87333489
## [116] -15.09992357 -12.62643465 -18.67758995 -19.68004587 -37.48560857
## [121] -17.81305922 -12.66202206 -19.30271343 -21.72957991 -22.55845982
## [126] -21.52415563 -20.24794907 -13.90309819 -9.72314701 -5.61385351
## [131] -19.19559151 -14.60050855 0.59948099 -18.38102178 -11.89805078
## [136] -7.15862084 -10.36967634 -11.72153497 -15.75852898 -23.71658582
## [141] -16.81450851 -18.81539064 -16.21991566 -21.34753506 -19.89305247
## [146] -13.19212067 -14.09899848 -11.79975897 -7.67576366 -18.11440601
## [151] -12.20967807 0.30245405 -20.03790621 -22.07962076 -11.53962180
## [156] -12.43151991 -16.30598534 -25.14147098 -25.35866048 -18.42964502
## [161] -23.55702280 -28.51322067 -19.33715610 -18.72742675 -17.24528368
## [166] -39.81128192 -17.79421772 -23.42999233 -20.54481767 -18.03433446
## [171] -29.18400370 -16.56620406 -25.05958813 -26.86366360 -18.25892162
## [176] -19.95062878 -27.09251048 -16.81362766 -17.24721745 -16.28739412
## [181] -26.70932956 -23.54301604 -20.51068135 -21.86569677 -11.93944425
## [186] -16.62000644 -11.36231656 -18.63231082 -24.52936419 -4.36589597
## [191] -34.61520336 -15.91096538 -10.20266170 -23.05211137 -13.39426968
## [196] -24.33209925 -19.01332253 -22.59241833 -16.30291101 -19.64552142
## [201] -16.70147037 -16.82160791 -17.89532465 -18.40079206 -14.43032019
## [206] -13.23805791 -18.69424522 -18.47302291 -6.63751350 -26.08750074
## [211] -15.86782708 -13.99952590 -20.13650685 -17.41470506 -21.51095305
## [216] -26.42437624 -27.64556986 -24.46482622 -24.92564656 -15.52958665
## [221] -14.41204339 -27.65095248 -21.91534638 -22.41475464 -21.13152584
## [226] -21.95175792 -25.65613518 -16.69717252
##
## $dbz
## [1] -0.34308511 -0.25125156 -0.05833605 0.27929749 0.79218188
## [6] 1.47922182 2.30485524 3.21303748 4.14584144 5.05543975
## [11] 5.90753205 6.67971713 7.35831080 7.93539606 8.40663124
## [16] 8.76979050 9.02386426 9.16855962 9.20409523 9.13124290
## [21] 8.95162362 8.66831954 8.28691883 7.81715134 7.27524331
## [26] 6.68687318 6.08988071 5.53447380 5.07729130 4.76703154
## [31] 4.62619135 4.64100032 4.76797325 4.95149532 5.13986675
## [36] 5.29318096 5.38425539 5.39634014 5.32026212 5.15214643
## [41] 4.89198455 4.54299904 4.11169474 3.60849581 3.04883250
## [46] 2.45437471 1.85374214 1.28151514 0.77416165 0.36246617
## [51] 0.06262932 -0.12933760 -0.23626124 -0.29239607 -0.33447723
## [56] -0.39520605 -0.50026438 -0.66787840 -0.90949582 -1.23051957
## [61] -1.63050787 -2.10255568 -2.63178678 -3.19322466 -3.75005016
## [66] -4.25448944 -4.65447399 -4.90735831 -4.99575022 -4.93499160
## [71] -4.76622446 -4.54063839 -4.30540157 -4.09652313 -3.93751787
## [76] -3.84070142 -3.80879522 -3.83582105 -3.90716419 -3.99931048
## [81] -4.08037668 -4.11306687 -4.06137444 -3.90023355 -3.62400906
## [86] -3.24863171 -2.80593011 -2.33401115 -1.86893653 -1.44025820
## [91] -1.07000408 -0.77358064 -0.56130747 -0.43989232 -0.41359259
## [96] -0.48502788 -0.65568424 -0.92615764 -1.29616336 -1.76430696
## [101] -2.32758018 -2.98051676 -3.71393866 -4.51328543 -5.35673796
## [106] -6.21383831 -7.04606439 -7.81132203 -8.47324413 -9.01258402
## [111] -9.43423257 -9.76470117 -10.04164760 -10.30192303 -10.57313115
## [116] -10.86942927 -11.18990402 -11.51803313 -11.82225258 -12.05939383
## [121] -12.18343603 -12.15958008 -11.97793914 -11.65795208 -11.24035868
## [126] -10.77309935 -10.29982273 -9.85457520 -9.46133590 -9.13576984
## [131] -8.88737401 -8.72120838 -8.63900146 -8.63965575 -8.71923220
## [136] -8.87049228 -9.08209642 -9.33765528 -9.61505019 -9.88676467
## [141] -10.12219926 -10.29259332 -10.37779367 -10.37219021 -10.28656303
## [146] -10.14470063 -9.97684947 -9.81334275 -9.68052655 -9.59920141
## [151] -9.58475394 -9.64805412 -9.79649944 -10.03489918 -10.36608398
## [156] -10.79120880 -11.30973334 -11.91904469 -12.61365732 -13.38391025
## [161] -14.21413395 -15.08048448 -15.94919127 -16.77687248 -17.51526828
## [166] -18.12159837 -18.57144217 -18.86643142 -19.03076919 -19.09894484
## [171] -19.10267953 -19.06291725 -18.98762087 -18.87358717 -18.71053455
## [176] -18.48632448 -18.19225295 -17.82706921 -17.39850904 -16.92206246
## [181] -16.41789369 -15.90739251 -15.41049576 -14.94417762 -14.52193691
## [186] -14.15389728 -13.84716926 -13.60624105 -13.43327228 -13.32823693
## [191] -13.28890281 -13.31066316 -13.38626766 -13.50554877 -13.65531243
## [196] -13.81964459 -13.98092530 -14.12174268 -14.22757260 -14.28959331
## [201] -14.30664053 -14.28546464 -14.23916996 -14.18452146 -14.13913217
## [206] -14.11928991 -14.13868153 -14.20788498 -14.33434393 -14.52255376
## [211] -14.77426875 -15.08862318 -15.46212383 -15.88852170 -16.35861886
## [216] -16.86012492 -17.37774411 -17.89372637 -18.38909533 -18.84559777
## [221] -19.24808254 -19.58664249 -19.85772197 -20.06371239 -20.21119143
## [226] -20.30848065 -20.36328768 -20.38092874
Acf(train.2012.june$count, lag.max = 50)
plotts.parzen.wge(train.2012.june$count)
## $freq
## [1] 0.002192982 0.004385965 0.006578947 0.008771930 0.010964912 0.013157895
## [7] 0.015350877 0.017543860 0.019736842 0.021929825 0.024122807 0.026315789
## [13] 0.028508772 0.030701754 0.032894737 0.035087719 0.037280702 0.039473684
## [19] 0.041666667 0.043859649 0.046052632 0.048245614 0.050438596 0.052631579
## [25] 0.054824561 0.057017544 0.059210526 0.061403509 0.063596491 0.065789474
## [31] 0.067982456 0.070175439 0.072368421 0.074561404 0.076754386 0.078947368
## [37] 0.081140351 0.083333333 0.085526316 0.087719298 0.089912281 0.092105263
## [43] 0.094298246 0.096491228 0.098684211 0.100877193 0.103070175 0.105263158
## [49] 0.107456140 0.109649123 0.111842105 0.114035088 0.116228070 0.118421053
## [55] 0.120614035 0.122807018 0.125000000 0.127192982 0.129385965 0.131578947
## [61] 0.133771930 0.135964912 0.138157895 0.140350877 0.142543860 0.144736842
## [67] 0.146929825 0.149122807 0.151315789 0.153508772 0.155701754 0.157894737
## [73] 0.160087719 0.162280702 0.164473684 0.166666667 0.168859649 0.171052632
## [79] 0.173245614 0.175438596 0.177631579 0.179824561 0.182017544 0.184210526
## [85] 0.186403509 0.188596491 0.190789474 0.192982456 0.195175439 0.197368421
## [91] 0.199561404 0.201754386 0.203947368 0.206140351 0.208333333 0.210526316
## [97] 0.212719298 0.214912281 0.217105263 0.219298246 0.221491228 0.223684211
## [103] 0.225877193 0.228070175 0.230263158 0.232456140 0.234649123 0.236842105
## [109] 0.239035088 0.241228070 0.243421053 0.245614035 0.247807018 0.250000000
## [115] 0.252192982 0.254385965 0.256578947 0.258771930 0.260964912 0.263157895
## [121] 0.265350877 0.267543860 0.269736842 0.271929825 0.274122807 0.276315789
## [127] 0.278508772 0.280701754 0.282894737 0.285087719 0.287280702 0.289473684
## [133] 0.291666667 0.293859649 0.296052632 0.298245614 0.300438596 0.302631579
## [139] 0.304824561 0.307017544 0.309210526 0.311403509 0.313596491 0.315789474
## [145] 0.317982456 0.320175439 0.322368421 0.324561404 0.326754386 0.328947368
## [151] 0.331140351 0.333333333 0.335526316 0.337719298 0.339912281 0.342105263
## [157] 0.344298246 0.346491228 0.348684211 0.350877193 0.353070175 0.355263158
## [163] 0.357456140 0.359649123 0.361842105 0.364035088 0.366228070 0.368421053
## [169] 0.370614035 0.372807018 0.375000000 0.377192982 0.379385965 0.381578947
## [175] 0.383771930 0.385964912 0.388157895 0.390350877 0.392543860 0.394736842
## [181] 0.396929825 0.399122807 0.401315789 0.403508772 0.405701754 0.407894737
## [187] 0.410087719 0.412280702 0.414473684 0.416666667 0.418859649 0.421052632
## [193] 0.423245614 0.425438596 0.427631579 0.429824561 0.432017544 0.434210526
## [199] 0.436403509 0.438596491 0.440789474 0.442982456 0.445175439 0.447368421
## [205] 0.449561404 0.451754386 0.453947368 0.456140351 0.458333333 0.460526316
## [211] 0.462719298 0.464912281 0.467105263 0.469298246 0.471491228 0.473684211
## [217] 0.475877193 0.478070175 0.480263158 0.482456140 0.484649123 0.486842105
## [223] 0.489035088 0.491228070 0.493421053 0.495614035 0.497807018 0.500000000
##
## $db
## [1] -4.80083688 1.73342930 2.95912507 -8.92683985 -8.69073421
## [6] -5.66744729 2.94645627 -3.35250420 2.11975229 -2.34448113
## [11] -4.79856214 -2.57332785 -12.19521424 0.77418576 -0.34262160
## [16] 4.64444849 -6.33193241 -4.81482165 20.49417880 -5.16165867
## [21] -2.79857225 2.39701596 -13.25644029 -10.03861616 -2.55903082
## [26] -2.75691994 -3.24578552 -6.83013406 -11.03850134 -16.10784667
## [31] -17.06518317 -6.93981202 5.88179973 1.17468825 9.74665038
## [36] 2.58254416 0.88803320 14.04606652 -1.22326834 2.30809642
## [41] 7.78739671 -0.95766747 2.74212477 -1.98262810 -14.20858749
## [46] -18.15232404 -9.29856734 -13.48263068 -4.46252096 -11.83475173
## [51] -4.15609522 -1.85859776 -9.69423024 -2.50105261 -5.01382094
## [56] -5.17140433 9.17446380 -15.08544252 -9.93327318 0.62351328
## [61] -5.69921245 -5.58796163 -13.31053346 -21.72562613 -8.95851291
## [66] -20.42546777 -12.23537556 -15.74587653 -15.22595232 -10.51304770
## [71] -9.09719326 -11.33061737 -1.60677375 -14.89905898 -14.90762213
## [76] 5.50205224 -9.21424894 -4.09548557 -2.80172718 -10.15956755
## [81] -5.76756475 -10.44116910 -16.16036343 -11.63004726 -10.18053450
## [86] -13.75559850 -10.24599621 -21.06588811 -7.38865741 -2.32618833
## [91] -10.72133135 0.69976441 -4.68631873 -11.17618178 9.85357239
## [96] -18.12838344 -5.56789139 -0.02963042 -6.66657705 -3.02233722
## [101] -17.01439209 -24.16596079 -13.30802867 -21.03290775 -20.00637067
## [106] -13.98763122 -17.05282259 -7.76858271 -11.56386807 -29.11448395
## [111] -11.93514820 -14.04054133 -14.34497743 -1.80896074 -11.87333489
## [116] -15.09992357 -12.62643465 -18.67758995 -19.68004587 -37.48560857
## [121] -17.81305922 -12.66202206 -19.30271343 -21.72957991 -22.55845982
## [126] -21.52415563 -20.24794907 -13.90309819 -9.72314701 -5.61385351
## [131] -19.19559151 -14.60050855 0.59948099 -18.38102178 -11.89805078
## [136] -7.15862084 -10.36967634 -11.72153497 -15.75852898 -23.71658582
## [141] -16.81450851 -18.81539064 -16.21991566 -21.34753506 -19.89305247
## [146] -13.19212067 -14.09899848 -11.79975897 -7.67576366 -18.11440601
## [151] -12.20967807 0.30245405 -20.03790621 -22.07962076 -11.53962180
## [156] -12.43151991 -16.30598534 -25.14147098 -25.35866048 -18.42964502
## [161] -23.55702280 -28.51322067 -19.33715610 -18.72742675 -17.24528368
## [166] -39.81128192 -17.79421772 -23.42999233 -20.54481767 -18.03433446
## [171] -29.18400370 -16.56620406 -25.05958813 -26.86366360 -18.25892162
## [176] -19.95062878 -27.09251048 -16.81362766 -17.24721745 -16.28739412
## [181] -26.70932956 -23.54301604 -20.51068135 -21.86569677 -11.93944425
## [186] -16.62000644 -11.36231656 -18.63231082 -24.52936419 -4.36589597
## [191] -34.61520336 -15.91096538 -10.20266170 -23.05211137 -13.39426968
## [196] -24.33209925 -19.01332253 -22.59241833 -16.30291101 -19.64552142
## [201] -16.70147037 -16.82160791 -17.89532465 -18.40079206 -14.43032019
## [206] -13.23805791 -18.69424522 -18.47302291 -6.63751350 -26.08750074
## [211] -15.86782708 -13.99952590 -20.13650685 -17.41470506 -21.51095305
## [216] -26.42437624 -27.64556986 -24.46482622 -24.92564656 -15.52958665
## [221] -14.41204339 -27.65095248 -21.91534638 -22.41475464 -21.13152584
## [226] -21.95175792 -25.65613518 -16.69717252
##
## $dbz
## [1] -0.34308511 -0.25125156 -0.05833605 0.27929749 0.79218188
## [6] 1.47922182 2.30485524 3.21303748 4.14584144 5.05543975
## [11] 5.90753205 6.67971713 7.35831080 7.93539606 8.40663124
## [16] 8.76979050 9.02386426 9.16855962 9.20409523 9.13124290
## [21] 8.95162362 8.66831954 8.28691883 7.81715134 7.27524331
## [26] 6.68687318 6.08988071 5.53447380 5.07729130 4.76703154
## [31] 4.62619135 4.64100032 4.76797325 4.95149532 5.13986675
## [36] 5.29318096 5.38425539 5.39634014 5.32026212 5.15214643
## [41] 4.89198455 4.54299904 4.11169474 3.60849581 3.04883250
## [46] 2.45437471 1.85374214 1.28151514 0.77416165 0.36246617
## [51] 0.06262932 -0.12933760 -0.23626124 -0.29239607 -0.33447723
## [56] -0.39520605 -0.50026438 -0.66787840 -0.90949582 -1.23051957
## [61] -1.63050787 -2.10255568 -2.63178678 -3.19322466 -3.75005016
## [66] -4.25448944 -4.65447399 -4.90735831 -4.99575022 -4.93499160
## [71] -4.76622446 -4.54063839 -4.30540157 -4.09652313 -3.93751787
## [76] -3.84070142 -3.80879522 -3.83582105 -3.90716419 -3.99931048
## [81] -4.08037668 -4.11306687 -4.06137444 -3.90023355 -3.62400906
## [86] -3.24863171 -2.80593011 -2.33401115 -1.86893653 -1.44025820
## [91] -1.07000408 -0.77358064 -0.56130747 -0.43989232 -0.41359259
## [96] -0.48502788 -0.65568424 -0.92615764 -1.29616336 -1.76430696
## [101] -2.32758018 -2.98051676 -3.71393866 -4.51328543 -5.35673796
## [106] -6.21383831 -7.04606439 -7.81132203 -8.47324413 -9.01258402
## [111] -9.43423257 -9.76470117 -10.04164760 -10.30192303 -10.57313115
## [116] -10.86942927 -11.18990402 -11.51803313 -11.82225258 -12.05939383
## [121] -12.18343603 -12.15958008 -11.97793914 -11.65795208 -11.24035868
## [126] -10.77309935 -10.29982273 -9.85457520 -9.46133590 -9.13576984
## [131] -8.88737401 -8.72120838 -8.63900146 -8.63965575 -8.71923220
## [136] -8.87049228 -9.08209642 -9.33765528 -9.61505019 -9.88676467
## [141] -10.12219926 -10.29259332 -10.37779367 -10.37219021 -10.28656303
## [146] -10.14470063 -9.97684947 -9.81334275 -9.68052655 -9.59920141
## [151] -9.58475394 -9.64805412 -9.79649944 -10.03489918 -10.36608398
## [156] -10.79120880 -11.30973334 -11.91904469 -12.61365732 -13.38391025
## [161] -14.21413395 -15.08048448 -15.94919127 -16.77687248 -17.51526828
## [166] -18.12159837 -18.57144217 -18.86643142 -19.03076919 -19.09894484
## [171] -19.10267953 -19.06291725 -18.98762087 -18.87358717 -18.71053455
## [176] -18.48632448 -18.19225295 -17.82706921 -17.39850904 -16.92206246
## [181] -16.41789369 -15.90739251 -15.41049576 -14.94417762 -14.52193691
## [186] -14.15389728 -13.84716926 -13.60624105 -13.43327228 -13.32823693
## [191] -13.28890281 -13.31066316 -13.38626766 -13.50554877 -13.65531243
## [196] -13.81964459 -13.98092530 -14.12174268 -14.22757260 -14.28959331
## [201] -14.30664053 -14.28546464 -14.23916996 -14.18452146 -14.13913217
## [206] -14.11928991 -14.13868153 -14.20788498 -14.33434393 -14.52255376
## [211] -14.77426875 -15.08862318 -15.46212383 -15.88852170 -16.35861886
## [216] -16.86012492 -17.37774411 -17.89372637 -18.38909533 -18.84559777
## [221] -19.24808254 -19.58664249 -19.85772197 -20.06371239 -20.21119143
## [226] -20.30848065 -20.36328768 -20.38092874
##
## $dbz1
## [1] -0.34308511 -0.25125156 -0.05833605 0.27929749 0.79218188
## [6] 1.47922182 2.30485524 3.21303748 4.14584144 5.05543975
## [11] 5.90753205 6.67971713 7.35831080 7.93539606 8.40663124
## [16] 8.76979050 9.02386426 9.16855962 9.20409523 9.13124290
## [21] 8.95162362 8.66831954 8.28691883 7.81715134 7.27524331
## [26] 6.68687318 6.08988071 5.53447380 5.07729130 4.76703154
## [31] 4.62619135 4.64100032 4.76797325 4.95149532 5.13986675
## [36] 5.29318096 5.38425539 5.39634014 5.32026212 5.15214643
## [41] 4.89198455 4.54299904 4.11169474 3.60849581 3.04883250
## [46] 2.45437471 1.85374214 1.28151514 0.77416165 0.36246617
## [51] 0.06262932 -0.12933760 -0.23626124 -0.29239607 -0.33447723
## [56] -0.39520605 -0.50026438 -0.66787840 -0.90949582 -1.23051957
## [61] -1.63050787 -2.10255568 -2.63178678 -3.19322466 -3.75005016
## [66] -4.25448944 -4.65447399 -4.90735831 -4.99575022 -4.93499160
## [71] -4.76622446 -4.54063839 -4.30540157 -4.09652313 -3.93751787
## [76] -3.84070142 -3.80879522 -3.83582105 -3.90716419 -3.99931048
## [81] -4.08037668 -4.11306687 -4.06137444 -3.90023355 -3.62400906
## [86] -3.24863171 -2.80593011 -2.33401115 -1.86893653 -1.44025820
## [91] -1.07000408 -0.77358064 -0.56130747 -0.43989232 -0.41359259
## [96] -0.48502788 -0.65568424 -0.92615764 -1.29616336 -1.76430696
## [101] -2.32758018 -2.98051676 -3.71393866 -4.51328543 -5.35673796
## [106] -6.21383831 -7.04606439 -7.81132203 -8.47324413 -9.01258402
## [111] -9.43423257 -9.76470117 -10.04164760 -10.30192303 -10.57313115
## [116] -10.86942927 -11.18990402 -11.51803313 -11.82225258 -12.05939383
## [121] -12.18343603 -12.15958008 -11.97793914 -11.65795208 -11.24035868
## [126] -10.77309935 -10.29982273 -9.85457520 -9.46133590 -9.13576984
## [131] -8.88737401 -8.72120838 -8.63900146 -8.63965575 -8.71923220
## [136] -8.87049228 -9.08209642 -9.33765528 -9.61505019 -9.88676467
## [141] -10.12219926 -10.29259332 -10.37779367 -10.37219021 -10.28656303
## [146] -10.14470063 -9.97684947 -9.81334275 -9.68052655 -9.59920141
## [151] -9.58475394 -9.64805412 -9.79649944 -10.03489918 -10.36608398
## [156] -10.79120880 -11.30973334 -11.91904469 -12.61365732 -13.38391025
## [161] -14.21413395 -15.08048448 -15.94919127 -16.77687248 -17.51526828
## [166] -18.12159837 -18.57144217 -18.86643142 -19.03076919 -19.09894484
## [171] -19.10267953 -19.06291725 -18.98762087 -18.87358717 -18.71053455
## [176] -18.48632448 -18.19225295 -17.82706921 -17.39850904 -16.92206246
## [181] -16.41789369 -15.90739251 -15.41049576 -14.94417762 -14.52193691
## [186] -14.15389728 -13.84716926 -13.60624105 -13.43327228 -13.32823693
## [191] -13.28890281 -13.31066316 -13.38626766 -13.50554877 -13.65531243
## [196] -13.81964459 -13.98092530 -14.12174268 -14.22757260 -14.28959331
## [201] -14.30664053 -14.28546464 -14.23916996 -14.18452146 -14.13913217
## [206] -14.11928991 -14.13868153 -14.20788498 -14.33434393 -14.52255376
## [211] -14.77426875 -15.08862318 -15.46212383 -15.88852170 -16.35861886
## [216] -16.86012492 -17.37774411 -17.89372637 -18.38909533 -18.84559777
## [221] -19.24808254 -19.58664249 -19.85772197 -20.06371239 -20.21119143
## [226] -20.30848065 -20.36328768 -20.38092874
##
## $dbz2
## [1] -0.34308511 -0.25125156 -0.05833605 0.27929749 0.79218188
## [6] 1.47922182 2.30485524 3.21303748 4.14584144 5.05543975
## [11] 5.90753205 6.67971713 7.35831080 7.93539606 8.40663124
## [16] 8.76979050 9.02386426 9.16855962 9.20409523 9.13124290
## [21] 8.95162362 8.66831954 8.28691883 7.81715134 7.27524331
## [26] 6.68687318 6.08988071 5.53447380 5.07729130 4.76703154
## [31] 4.62619135 4.64100032 4.76797325 4.95149532 5.13986675
## [36] 5.29318096 5.38425539 5.39634014 5.32026212 5.15214643
## [41] 4.89198455 4.54299904 4.11169474 3.60849581 3.04883250
## [46] 2.45437471 1.85374214 1.28151514 0.77416165 0.36246617
## [51] 0.06262932 -0.12933760 -0.23626124 -0.29239607 -0.33447723
## [56] -0.39520605 -0.50026438 -0.66787840 -0.90949582 -1.23051957
## [61] -1.63050787 -2.10255568 -2.63178678 -3.19322466 -3.75005016
## [66] -4.25448944 -4.65447399 -4.90735831 -4.99575022 -4.93499160
## [71] -4.76622446 -4.54063839 -4.30540157 -4.09652313 -3.93751787
## [76] -3.84070142 -3.80879522 -3.83582105 -3.90716419 -3.99931048
## [81] -4.08037668 -4.11306687 -4.06137444 -3.90023355 -3.62400906
## [86] -3.24863171 -2.80593011 -2.33401115 -1.86893653 -1.44025820
## [91] -1.07000408 -0.77358064 -0.56130747 -0.43989232 -0.41359259
## [96] -0.48502788 -0.65568424 -0.92615764 -1.29616336 -1.76430696
## [101] -2.32758018 -2.98051676 -3.71393866 -4.51328543 -5.35673796
## [106] -6.21383831 -7.04606439 -7.81132203 -8.47324413 -9.01258402
## [111] -9.43423257 -9.76470117 -10.04164760 -10.30192303 -10.57313115
## [116] -10.86942927 -11.18990402 -11.51803313 -11.82225258 -12.05939383
## [121] -12.18343603 -12.15958008 -11.97793914 -11.65795208 -11.24035868
## [126] -10.77309935 -10.29982273 -9.85457520 -9.46133590 -9.13576984
## [131] -8.88737401 -8.72120838 -8.63900146 -8.63965575 -8.71923220
## [136] -8.87049228 -9.08209642 -9.33765528 -9.61505019 -9.88676467
## [141] -10.12219926 -10.29259332 -10.37779367 -10.37219021 -10.28656303
## [146] -10.14470063 -9.97684947 -9.81334275 -9.68052655 -9.59920141
## [151] -9.58475394 -9.64805412 -9.79649944 -10.03489918 -10.36608398
## [156] -10.79120880 -11.30973334 -11.91904469 -12.61365732 -13.38391025
## [161] -14.21413395 -15.08048448 -15.94919127 -16.77687248 -17.51526828
## [166] -18.12159837 -18.57144217 -18.86643142 -19.03076919 -19.09894484
## [171] -19.10267953 -19.06291725 -18.98762087 -18.87358717 -18.71053455
## [176] -18.48632448 -18.19225295 -17.82706921 -17.39850904 -16.92206246
## [181] -16.41789369 -15.90739251 -15.41049576 -14.94417762 -14.52193691
## [186] -14.15389728 -13.84716926 -13.60624105 -13.43327228 -13.32823693
## [191] -13.28890281 -13.31066316 -13.38626766 -13.50554877 -13.65531243
## [196] -13.81964459 -13.98092530 -14.12174268 -14.22757260 -14.28959331
## [201] -14.30664053 -14.28546464 -14.23916996 -14.18452146 -14.13913217
## [206] -14.11928991 -14.13868153 -14.20788498 -14.33434393 -14.52255376
## [211] -14.77426875 -15.08862318 -15.46212383 -15.88852170 -16.35861886
## [216] -16.86012492 -17.37774411 -17.89372637 -18.38909533 -18.84559777
## [221] -19.24808254 -19.58664249 -19.85772197 -20.06371239 -20.21119143
## [226] -20.30848065 -20.36328768 -20.38092874
count.d1 = artrans.wge(train.2012.june$count, phi.tr = 1)
plotts.sample.wge(count.d1)
## $autplt
## [1] 1.000000000 0.327893791 -0.171539952 -0.172088845 -0.014890287
## [6] 0.029755069 -0.106796549 -0.272576678 -0.274992466 0.133282685
## [11] 0.187304506 -0.054467858 -0.168736650 -0.061550287 0.129642653
## [16] 0.086179712 -0.215608804 -0.233668505 -0.075308547 0.018255277
## [21] -0.008047202 -0.112419980 -0.106423281 0.265081883 0.674508859
## [26] 0.272600907
##
## $freq
## [1] 0.002197802 0.004395604 0.006593407 0.008791209 0.010989011 0.013186813
## [7] 0.015384615 0.017582418 0.019780220 0.021978022 0.024175824 0.026373626
## [13] 0.028571429 0.030769231 0.032967033 0.035164835 0.037362637 0.039560440
## [19] 0.041758242 0.043956044 0.046153846 0.048351648 0.050549451 0.052747253
## [25] 0.054945055 0.057142857 0.059340659 0.061538462 0.063736264 0.065934066
## [31] 0.068131868 0.070329670 0.072527473 0.074725275 0.076923077 0.079120879
## [37] 0.081318681 0.083516484 0.085714286 0.087912088 0.090109890 0.092307692
## [43] 0.094505495 0.096703297 0.098901099 0.101098901 0.103296703 0.105494505
## [49] 0.107692308 0.109890110 0.112087912 0.114285714 0.116483516 0.118681319
## [55] 0.120879121 0.123076923 0.125274725 0.127472527 0.129670330 0.131868132
## [61] 0.134065934 0.136263736 0.138461538 0.140659341 0.142857143 0.145054945
## [67] 0.147252747 0.149450549 0.151648352 0.153846154 0.156043956 0.158241758
## [73] 0.160439560 0.162637363 0.164835165 0.167032967 0.169230769 0.171428571
## [79] 0.173626374 0.175824176 0.178021978 0.180219780 0.182417582 0.184615385
## [85] 0.186813187 0.189010989 0.191208791 0.193406593 0.195604396 0.197802198
## [91] 0.200000000 0.202197802 0.204395604 0.206593407 0.208791209 0.210989011
## [97] 0.213186813 0.215384615 0.217582418 0.219780220 0.221978022 0.224175824
## [103] 0.226373626 0.228571429 0.230769231 0.232967033 0.235164835 0.237362637
## [109] 0.239560440 0.241758242 0.243956044 0.246153846 0.248351648 0.250549451
## [115] 0.252747253 0.254945055 0.257142857 0.259340659 0.261538462 0.263736264
## [121] 0.265934066 0.268131868 0.270329670 0.272527473 0.274725275 0.276923077
## [127] 0.279120879 0.281318681 0.283516484 0.285714286 0.287912088 0.290109890
## [133] 0.292307692 0.294505495 0.296703297 0.298901099 0.301098901 0.303296703
## [139] 0.305494505 0.307692308 0.309890110 0.312087912 0.314285714 0.316483516
## [145] 0.318681319 0.320879121 0.323076923 0.325274725 0.327472527 0.329670330
## [151] 0.331868132 0.334065934 0.336263736 0.338461538 0.340659341 0.342857143
## [157] 0.345054945 0.347252747 0.349450549 0.351648352 0.353846154 0.356043956
## [163] 0.358241758 0.360439560 0.362637363 0.364835165 0.367032967 0.369230769
## [169] 0.371428571 0.373626374 0.375824176 0.378021978 0.380219780 0.382417582
## [175] 0.384615385 0.386813187 0.389010989 0.391208791 0.393406593 0.395604396
## [181] 0.397802198 0.400000000 0.402197802 0.404395604 0.406593407 0.408791209
## [187] 0.410989011 0.413186813 0.415384615 0.417582418 0.419780220 0.421978022
## [193] 0.424175824 0.426373626 0.428571429 0.430769231 0.432967033 0.435164835
## [199] 0.437362637 0.439560440 0.441758242 0.443956044 0.446153846 0.448351648
## [205] 0.450549451 0.452747253 0.454945055 0.457142857 0.459340659 0.461538462
## [211] 0.463736264 0.465934066 0.468131868 0.470329670 0.472527473 0.474725275
## [217] 0.476923077 0.479120879 0.481318681 0.483516484 0.485714286 0.487912088
## [223] 0.490109890 0.492307692 0.494505495 0.496703297 0.498901099
##
## $db
## [1] -32.3367723 -25.5723506 -19.0131479 -33.0768532 -30.3409984 -24.3251385
## [7] -13.2972974 -18.8083756 -11.4505945 -15.2285807 -15.9062064 -13.0440112
## [13] -20.8022491 -8.2200123 -8.4392702 -2.8866783 -9.5702332 -8.5563544
## [19] 13.4001354 -7.7623653 -8.1552272 -3.8143275 -18.3359067 -13.0142968
## [25] -8.2427879 -7.3224488 -7.0588825 -10.7248532 -15.7087546 -18.2689705
## [31] -21.8357457 -5.8127905 2.6063668 -1.5620955 8.5010979 -0.1391599
## [37] 2.0977943 13.0036261 -7.3524164 2.8689623 6.6315084 -0.5503195
## [43] 3.9618451 -2.9628236 -17.8086304 -23.4148779 -7.9236659 -9.8649734
## [49] -2.1769563 -6.3424174 0.3318878 -3.3133235 -15.3244698 -1.2189806
## [55] -1.7963425 2.3280078 10.9518401 -19.0958650 -3.8912058 2.1009981
## [61] -2.4310021 -0.7448586 -15.7655129 -16.6993400 -5.7248672 -16.1068157
## [67] -10.8320000 -12.2772210 -13.4389960 -4.6504204 -8.8962411 -11.4140398
## [73] 3.1491173 -12.4527547 -4.6808983 10.3724827 -10.1260520 1.1935390
## [79] 1.3677698 -2.6567317 1.8698192 -5.2339181 -6.9402906 -15.7958484
## [85] -3.9878923 -8.6451190 -3.9530199 -10.3589194 2.1544363 -0.1283996
## [91] -19.3113602 6.6612707 2.9103633 6.6379131 15.5416075 -1.7031321
## [97] 2.1802491 4.8251506 0.2295480 5.7858923 -8.7207154 -6.1756800
## [103] -3.4183093 -6.3270509 -17.2554540 -8.9985969 -7.8626994 2.6404394
## [109] -11.1275591 -9.0939481 -9.0979020 -3.2869222 2.3741477 2.0196737
## [115] -5.4392616 -8.5167246 -4.5576017 -7.4763231 -6.5119259 -8.5714162
## [121] -9.3032649 -8.1633942 -16.2241705 -12.4002463 -10.4678968 -23.0231512
## [127] -6.3942100 -8.4938339 -9.0502737 2.8063745 -14.9336759 2.0964263
## [133] 8.5143904 -4.9694573 -0.3324924 -2.4876631 -1.6855697 0.6675653
## [139] -2.8252525 -3.6958549 -14.4258969 -11.3297101 -13.5365188 -11.8264357
## [145] -7.0193422 1.4943761 -9.5179299 -15.6361491 -0.2726094 -6.2696802
## [151] 5.6805016 7.3794792 -6.4859411 -5.6530875 -5.9163547 -4.0017723
## [157] -3.2157515 -7.7705516 -17.1561609 -6.5771332 -14.0778344 -18.1338858
## [163] -12.5607663 -7.5521202 -5.8525022 -14.2873385 -7.0585227 -6.0208469
## [169] -10.1294315 -4.5335597 -8.5563356 -11.5426940 -8.8747222 -12.0214577
## [175] -2.3994945 -10.4283928 -7.9481329 -7.2438085 -14.8854991 -14.0432652
## [181] -22.4151718 -7.8442841 -18.6504431 -3.6169068 -15.1939502 -8.6052638
## [187] -2.8819611 -3.6664756 0.3988013 2.7332175 -15.8228929 -3.9151727
## [193] -1.2946230 -7.1547507 -1.4020267 -3.6533556 -18.8994847 -4.8433807
## [199] -9.0864001 -10.6505926 -8.0972313 -6.2078731 -1.2692168 -9.3214436
## [205] 1.0991626 -17.4857158 -2.3791758 1.9495735 -2.3415388 -6.1674358
## [211] -35.5415711 -2.9193221 -5.7913755 -11.3105597 -22.7193544 -19.7407883
## [217] -10.0524034 -19.4853379 -5.0201761 -18.5832126 -6.3094403 -22.7397576
## [223] -15.5217280 -8.6309794 -21.4724303 -10.6914246 -9.9982721
##
## $dbz
## [1] -16.14422598 -15.09898543 -13.58316668 -11.82796448 -10.01720537
## [6] -8.26485473 -6.62982957 -5.13752236 -3.79556598 -2.60309234
## [11] -1.55564577 -0.64763596 0.12651406 0.77189838 1.29301976
## [16] 1.69389502 1.97832444 2.15033766 2.21487880 2.17883784
## [21] 2.05256605 1.85198412 1.60118879 1.33488349 1.09884018
## [26] 0.94542098 0.92192981 1.05460585 1.33774150 1.73643692
## [31] 2.20072503 2.68079761 3.13598663 3.53708873 3.86495816
## [36] 4.10799464 4.25986407 4.31787814 4.28205665 4.15478976
## [41] 3.94102810 3.64896060 3.29113209 2.88584349 2.45838686
## [46] 2.04116502 1.67125489 1.38423718 1.20506773 1.13988378
## [51] 1.17374610 1.27589107 1.40899717 1.53744031 1.63194359
## [56] 1.67091174 1.63992938 1.53074340 1.34051635 1.07173324
## [61] 0.73292345 0.34018940 -0.08079380 -0.49336165 -0.85119476
## [66] -1.10518715 -1.21655522 -1.17113058 -0.98539775 -0.69946763
## [71] -0.36246579 -0.01967458 0.29403964 0.55555703 0.75243080
## [76] 0.88152367 0.94832262 0.96708061 0.96132274 0.96359878
## [81] 1.01273685 1.14702844 1.39393167 1.76061140 2.23118146
## [86] 2.77257511 3.34492669 3.91059789 4.43896452 4.90743517
## [91] 5.30041695 5.60763761 5.82256170 5.94115824 5.96104437
## [96] 5.88095196 5.70045924 5.41995237 5.04081316 4.56586168
## [101] 4.00011195 3.35191040 2.63448580 1.86777170 1.07995672
## [106] 0.30753149 -0.40802620 -1.02825057 -1.52877664 -1.90790487
## [111] -2.18670375 -2.40033525 -2.58619813 -2.77459816 -2.98372582
## [116] -3.21770303 -3.46602199 -3.70384272 -3.89419961 -3.99421595
## [121] -3.96639457 -3.79190115 -3.47847553 -3.05747283 -2.57251770
## [126] -2.06745068 -1.57894987 -1.13427991 -0.75209904 -0.44431140
## [131] -0.21784064 -0.07590248 -0.01869911 -0.04357207 -0.14466860
## [136] -0.31218685 -0.53133456 -0.78132669 -1.03509125 -1.26073689
## [141] -1.42581991 -1.50435053 -1.48425778 -1.37142179 -1.18774169
## [146] -0.96449207 -0.73477096 -0.52813346 -0.36821245 -0.27254285
## [151] -0.25346904 -0.31932813 -0.47549575 -0.72513880 -1.06963807
## [156] -1.50867399 -2.03995378 -2.65852604 -3.35560385 -4.11684417
## [161] -4.92020074 -5.73392958 -6.51618239 -7.21850986 -7.79509895
## [166] -8.21592175 -8.47672331 -8.59847601 -8.61650079 -8.56681346
## [171] -8.47666124 -8.36099239 -8.22317763 -8.05794939 -7.85535073
## [176] -7.60503642 -7.30025736 -6.94066660 -6.53322715 -6.09114051
## [181] -5.63147115 -5.17248392 -4.73149571 -4.32356170 -3.96091863
## [186] -3.65292978 -3.40627052 -3.22516091 -3.11152655 -3.06502439
## [191] -3.08290871 -3.15974530 -3.28702644 -3.45281140 -3.64162327
## [196] -3.83494712 -4.01270788 -4.15590839 -4.25007846 -4.28850171
## [201] -4.27388086 -4.21764102 -4.13721116 -4.05250136 -3.98282218
## [206] -3.94489314 -3.95194608 -4.01359101 -4.13606676 -4.32259427
## [211] -4.57366817 -4.88721320 -5.25859245 -5.68049909 -6.14280707
## [216] -6.63250922 -7.13392676 -7.62940424 -8.10064914 -8.53067931
## [221] -8.90601567 -9.21845964 -9.46577254 -9.65094766 -9.78033842
## [226] -9.86130274 -9.90003950
# aic5.wge(train.2012.june$count, p=0:2, q=0:2, type = "aic") # BIC picks ARMA (15,0)
# aic5.wge(train.2012.june$count, p=24:26, q=0:2, type = "aic") # BIC picks ARMA (25,1)
# aic5.wge(train.2012.june$count, p=26:30, q=0:2, type = "bic") # BIC picks ARMA (26,0)
# aic5.wge(train.2012.june$count, p=24:26, q=0:5, type = "bic") # BIC picks ARMA (26,0)
# aic5.wge(train.2012.june$count, p=24:26, q=0:2, type = "aic") # BIC picks ARMA (26,4)
# aic5.wge(train.2012.june$count, p=0:15, q=0:2, type = "aic") # AIC picks ARMA (15,1)
# aic5.wge(train.2012.june$count, p=15:25, q=0:2, type = "aic") # AIC picks ARMA (24,2)
# aic5.wge(train.2012.june$count, p=26:30, q=0:2, type = "aic") # AIC picks ARMA (30, 1)
# factor.wge(c=(rep(0,7), 1))
est.2012.june = est.arma.wge(train.2012.june$count, p=25, q=1)
##
## Coefficients of Original polynomial:
## 0.7955 -0.1486 -0.0433 0.0595 -0.0160 -0.0944 0.0933 -0.2967 0.3386 -0.0982 -0.1163 0.0587 -0.0345 -0.0496 0.0946 -0.1952 0.1623 -0.0468 -0.1032 0.0630 0.0025 -0.0638 0.1388 0.4465 -0.3114
##
## Factor Roots Abs Recip System Freq
## 1-1.9198B+0.9869B^2 0.9726+-0.2594i 0.9934 0.0415
## 1-0.5154B+0.9856B^2 0.2615+-0.9728i 0.9928 0.2082
## 1-1.7188B+0.9833B^2 0.8740+-0.5031i 0.9916 0.0831
## 1+0.9780B+0.9746B^2 -0.5018+-0.8799i 0.9872 0.3325
## 1-1.4029B+0.9669B^2 0.7254+-0.7127i 0.9833 0.1236
## 1+0.5181B+0.9665B^2 -0.2680+-0.9812i 0.9831 0.2924
## 1-0.9603B+0.9558B^2 0.5023+-0.8910i 0.9776 0.1683
## 1+1.6958B+0.9525B^2 -0.8902+-0.5074i 0.9760 0.4175
## 1+1.8749B+0.9463B^2 -0.9906+-0.2746i 0.9728 0.4570
## 1-0.0387B+0.9225B^2 0.0210+-1.0410i 0.9605 0.2468
## 1-0.9452B 1.0580 0.9452 0.0000
## 1+0.9201B -1.0869 0.9201 0.5000
## 1+1.3322B+0.8432B^2 -0.7900+-0.7496i 0.9182 0.3792
## 1-0.6135B 1.6299 0.6135 0.0000
##
##
est.2012.june$phi
## [1] 0.795515987 -0.148554531 -0.043325557 0.059479402 -0.016004669
## [6] -0.094380393 0.093261481 -0.296693810 0.338638046 -0.098216138
## [11] -0.116341969 0.058716888 -0.034474397 -0.049607645 0.094630835
## [16] -0.195217759 0.162268467 -0.046793836 -0.103169033 0.062992094
## [21] 0.002513806 -0.063828766 0.138763799 0.446471640 -0.311434209
est.2012.june$theta
## [1] -0.3030922
est.2012.june$avar
## [1] 5623.312
mean(train.2012.june$count)
## [1] 287.1864
\[\begin{equation} (1-0.80B+0.15B^2+0.04B^3-0.05B^4+0.02B^5+0.09B^6-0.09B^7+0.30B^8-0.34B^9+0.10B^{10}+0.12B^{11}-0.06B^{12}+0.03B^{13} + 0.05B^{14}-0.09B^{15}+0.20B^{16}-0.16B^{17}+0.05B^{18}+0.10B^{19}-0.06B^{20}-0.003B^{21}+0.06B^{22}-0.13B^{23}-0.45B^{24}+0.31B^{25})(X_t - 287.18) = (1+0.30B)a_t; \sigma^2 = 5623.31 \end{equation}\]
plotts.wge(est.2012.june$res)
# 7 day forecast
no_ahead = 24 * 7
len_of_obs = length(train.2012.june$datetime)
forecast.2012.june = fore.aruma.wge(train.2012.june$count, phi = est.2012.june$phi, theta = est.2012.june$theta, n.ahead = no_ahead, lastn = TRUE, limits = FALSE)
ase.2012.june = mean((train.2012.june$count[(len_of_obs - no_ahead + 1): len_of_obs] - forecast.2012.june$f)^2)
ase.2012.june
## [1] 29004.65
rmse.2012.june = RMSE(y_true = train.2012.june$count[(len_of_obs - no_ahead + 1): len_of_obs], y_pred = forecast.2012.june$f)
rmse.2012.june
## [1] 170.3075
predictions = round(forecast.2012.june$f)
actuals = train.2012.june$count[(len_of_obs - no_ahead + 1): len_of_obs]
preds.v.actuals.2012.june <- data.frame(predictions, actuals) # Apply data.frame function
preds.v.actuals.2012.june <- preds.v.actuals.2012.june %>%
mutate(diff = (round(predictions) - actuals)) %>%
mutate(abs.diff = abs(round(predictions) - actuals))
preds.v.actuals.2012.june
## predictions actuals diff abs.diff
## 1 21 34 -13 13
## 2 9 28 -19 19
## 3 95 4 91 91
## 4 134 8 126 126
## 5 113 10 103 103
## 6 158 40 118 118
## 7 220 194 26 26
## 8 364 505 -141 141
## 9 542 713 -171 171
## 10 335 352 -17 17
## 11 214 198 16 16
## 12 186 246 -60 60
## 13 187 334 -147 147
## 14 157 255 -98 98
## 15 145 320 -175 175
## 16 178 281 -103 103
## 17 280 392 -112 112
## 18 617 857 -240 240
## 19 630 744 -114 114
## 20 496 671 -175 175
## 21 404 448 -44 44
## 22 329 396 -67 67
## 23 269 238 31 31
## 24 169 153 16 16
## 25 80 48 32 32
## 26 43 21 22 22
## 27 139 9 130 130
## 28 192 5 187 187
## 29 176 6 170 170
## 30 203 40 163 163
## 31 249 181 68 68
## 32 365 506 -141 141
## 33 475 719 -244 244
## 34 339 357 -18 18
## 35 239 179 60 60
## 36 229 228 1 1
## 37 231 265 -34 34
## 38 199 284 -85 85
## 39 186 298 -112 112
## 40 203 324 -121 121
## 41 291 438 -147 147
## 42 547 867 -320 320
## 43 576 823 -247 247
## 44 471 579 -108 108
## 45 400 435 -35 35
## 46 348 337 11 11
## 47 296 242 54 54
## 48 209 172 37 37
## 49 118 94 24 24
## 50 71 51 20 20
## 51 157 15 142 142
## 52 219 5 214 214
## 53 209 14 195 195
## 54 223 33 190 190
## 55 260 151 109 109
## 56 352 430 -78 78
## 57 426 653 -227 227
## 58 333 366 -33 33
## 59 247 216 31 31
## 60 245 286 -41 41
## 61 253 403 -150 150
## 62 226 393 -167 167
## 63 211 376 -165 165
## 64 218 377 -159 159
## 65 295 558 -263 263
## 66 489 823 -334 334
## 67 523 693 -170 170
## 68 442 467 -25 25
## 69 388 385 3 3
## 70 353 333 20 20
## 71 309 321 -12 12
## 72 234 222 12 12
## 73 147 137 10 10
## 74 98 95 3 3
## 75 171 67 104 104
## 76 233 27 206 206
## 77 228 8 220 220
## 78 234 23 211 211
## 79 265 47 218 218
## 80 338 78 260 260
## 81 392 204 188 188
## 82 325 367 -42 42
## 83 251 435 -184 184
## 84 252 566 -314 314
## 85 265 603 -338 338
## 86 244 617 -373 373
## 87 229 573 -344 344
## 88 231 583 -352 352
## 89 295 542 -247 247
## 90 444 593 -149 149
## 91 478 571 -93 93
## 92 415 461 -46 46
## 93 374 352 22 22
## 94 353 290 63 63
## 95 316 280 36 36
## 96 251 183 68 68
## 97 172 148 24 24
## 98 125 88 37 37
## 99 184 74 110 110
## 100 241 28 213 213
## 101 239 18 221 221
## 102 242 17 225 225
## 103 268 23 245 245
## 104 328 48 280 280
## 105 368 119 249 249
## 106 319 274 45 45
## 107 255 436 -181 181
## 108 255 546 -291 291
## 109 271 615 -344 344
## 110 257 614 -357 357
## 111 242 582 -340 340
## 112 242 463 -221 221
## 113 295 580 -285 285
## 114 410 593 -183 183
## 115 441 513 -72 72
## 116 393 390 3 3
## 117 361 302 59 59
## 118 348 246 102 102
## 119 319 153 166 166
## 120 264 108 156 156
## 121 193 40 153 153
## 122 151 14 137 137
## 123 197 9 188 188
## 124 248 4 244 244
## 125 247 9 238 238
## 126 247 23 224 224
## 127 270 37 233 233
## 128 319 145 174 174
## 129 350 474 -124 124
## 130 313 250 63 63
## 131 259 91 168 168
## 132 258 121 137 137
## 133 275 168 107 107
## 134 267 225 42 42
## 135 253 219 34 34
## 136 251 237 14 14
## 137 295 332 -37 37
## 138 384 723 -339 339
## 139 412 642 -230 230
## 140 375 463 -88 88
## 141 350 362 -12 12
## 142 343 273 70 70
## 143 320 164 156 156
## 144 273 74 199 199
## 145 211 35 176 176
## 146 173 14 159 159
## 147 209 15 194 194
## 148 252 8 244 244
## 149 253 10 243 243
## 150 251 37 214 214
## 151 272 161 111 111
## 152 312 480 -168 168
## 153 337 673 -336 336
## 154 309 328 -19 19
## 155 263 180 83 83
## 156 261 230 31 31
## 157 278 292 -14 14
## 158 274 272 2 2
## 159 260 227 33 33
## 160 258 259 -1 1
## 161 294 334 -40 40
## 162 365 811 -446 446
## 163 389 795 -406 406
## 164 360 514 -154 154
## 165 339 458 -119 119
## 166 336 276 60 60
## 167 319 291 28 28
## 168 280 125 155 155
# 1 day forecast
no_ahead = 24
len_of_obs = length(train.2012.june$datetime)
forecast.2012.june = fore.aruma.wge(train.2012.june$count, phi = est.2012.june$phi, theta = est.2012.june$theta, n.ahead = no_ahead, lastn = TRUE, limits = FALSE)
ase.2012.june = mean((train.2012.june$count[(len_of_obs - no_ahead + 1): len_of_obs] - forecast.2012.june$f)^2)
ase.2012.june
## [1] 9397.58
rmse.2012.june = RMSE(y_true = train.2012.june$count[(len_of_obs - no_ahead + 1): len_of_obs], y_pred = forecast.2012.june$f)
rmse.2012.june
## [1] 96.94112
predictions = round(forecast.2012.june$f)
actuals = train.2012.june$count[(len_of_obs - no_ahead + 1): len_of_obs]
preds.v.actuals.2012.june <- data.frame(predictions, actuals) # Apply data.frame function
preds.v.actuals.2012.june <- preds.v.actuals.2012.june %>%
mutate(diff = (round(predictions) - actuals)) %>%
mutate(abs.diff = abs(round(predictions) - actuals))
preds.v.actuals.2012.june
## predictions actuals diff abs.diff
## 1 6 35 -29 29
## 2 -9 14 -23 23
## 3 98 15 83 83
## 4 114 8 106 106
## 5 105 10 95 95
## 6 125 37 88 88
## 7 148 161 -13 13
## 8 243 480 -237 237
## 9 429 673 -244 244
## 10 290 328 -38 38
## 11 189 180 9 9
## 12 218 230 -12 12
## 13 247 292 -45 45
## 14 276 272 4 4
## 15 284 227 57 57
## 16 290 259 31 31
## 17 357 334 23 23
## 18 648 811 -163 163
## 19 631 795 -164 164
## 20 476 514 -38 38
## 21 387 458 -71 71
## 22 313 276 37 37
## 23 237 291 -54 54
## 24 158 125 33 33
# series is the array of the series
# horizon is how far you want to predict into the future
# d is the order of the differencing: (1-B^)^d
# s is the order of the seasonality: (1-B^s)
# phis = order of the stationary AR term
# thetas = order of the invertible MA term
# It simply takes the given horizon and the model in the form of s,d,phis and
# thetas and figures out how many windows it can create in the data (series) and then calculates the ASE for each window.
#The output is the average off all the ASEs from each individual window.
roll.win.ase.wge = function(series, horizon = 1, s = 0, d = 0, phis = 0, thetas = 0)
{
trainingSize = length(phis) + length(thetas) + s + d + 1
numwindows = length(series)-(trainingSize + horizon) + 1
ASEHolder = numeric(numwindows)
print(paste("Please Hold For a Moment, TSWGE is processing the Rolling Window ASE with", numwindows, "windows."))
for( i in 1:numwindows)
{
invisible(capture.output(forecasts <- fore.aruma.wge(series[i:(i+(trainingSize-1))],phi = phis, theta = thetas, s = s, d = d,n.ahead = horizon)))
ASE = mean((series[(trainingSize+i):(trainingSize+ i + (horizon) - 1)] - forecasts$f)^2)
ASEHolder[i] = ASE
}
ASEHolder
hist(ASEHolder, main = "ASEs for Individual Windows")
WindowedASE = mean(ASEHolder)
print("The Summary Statistics for the Rolling Window ASE Are:")
print(summary(ASEHolder))
print(paste("The Rolling Window ASE is: ",round(WindowedASE,3)))
return(list(rwASE = WindowedASE, numwindows = numwindows, horizon = horizon, s = s, d = d, phis = phis, thetas = thetas))
}
roll.win.ase.wge(train.2012.june$count, horizon = 24*7, est.2012.june$phi, est.2012.june$theta, s = 0, d = 0)
## [1] "Please Hold For a Moment, TSWGE is processing the Rolling Window ASE with 262 windows."
## [1] "The Summary Statistics for the Rolling Window ASE Are:"
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 17625 22403 27033 30053 35911 70980
## [1] "The Rolling Window ASE is: 30052.647"
## $rwASE
## [1] 30052.65
##
## $numwindows
## [1] 262
##
## $horizon
## [1] 168
##
## $s
## [1] 0
##
## $d
## [1] 0
##
## $phis
## [1] 0.795515987 -0.148554531 -0.043325557 0.059479402 -0.016004669
## [6] -0.094380393 0.093261481 -0.296693810 0.338638046 -0.098216138
## [11] -0.116341969 0.058716888 -0.034474397 -0.049607645 0.094630835
## [16] -0.195217759 0.162268467 -0.046793836 -0.103169033 0.062992094
## [21] 0.002513806 -0.063828766 0.138763799 0.446471640 -0.311434209
##
## $thetas
## [1] -0.3030922